Details

Time bar (total: 47.5s)

sample140.0ms

Algorithm
intervals
Results
33.0ms187×body80valid
28.0ms34×body2560valid
23.0ms35×body1280valid
14.0ms115×body80nan
10.0ms18×body640valid
4.0ms5×body5120valid
2.0ms4×body320valid
1.0ms5×body160valid

simplify159.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
158.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 35.5b

localize39.0ms

Local error

Found 4 expressions with local error:

24.0b
(sqrt (- (* b b) (* (* 3 a) c)))
1.2b
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
0.4b
(- (* b b) (* (* 3 a) c))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×fma-def add-cube-cbrt add-log-exp
9×add-cbrt-cube add-exp-log
6×distribute-rgt-neg-in distribute-lft-out
5×pow1 times-frac associate-/l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×distribute-lft-neg-in sqrt-prod
2×neg-sub0 cbrt-undiv sum-log flip3-+ flip3-- sqrt-div div-exp associate-+l- flip-+ flip-- associate-/l/
1×+-commutative rem-sqrt-square clear-num associate-/r* neg-mul-1 sub-neg frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff neg-log prod-exp cbrt-unprod div-inv
Counts
4 → 94
Calls
4 calls:
Slowest
55.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
19.0ms
(- (* b b) (* (* 3 a) c))
14.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
9.0ms
(sqrt (- (* b b) (* (* 3 a) c)))

series481.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
180.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
124.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
104.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
72.0ms
(- (* b b) (* (* 3 a) c))

simplify5.2s

Counts
52 → 106
Calls
52 calls:
Slowest
568.0ms
(- (* (- b) (- b)) (* (sqrt (- (* b b) (* (* 3 a) c))) (sqrt (- (* b b) (* (* 3 a) c)))))
387.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))
363.0ms
(/ (* (* (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))) (+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))) (* (* (* 3 a) (* 3 a)) (* 3 a)))
313.0ms
(/ (exp (* b b)) (exp (* (* 3 a) c)))
244.0ms
(/ (* (* (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))) (+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))) (* (* (* 3 3) 3) (* (* a a) a)))

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize63.0ms

Local error

Found 4 expressions with local error:

24.0b
(sqrt (- (* b b) (* (* 3 a) c)))
16.8b
(/ (* 3 (* c a)) (* (* 3 a) (- (- b) (sqrt (- (* b b) (* (* 3 a) c))))))
0.4b
(- (* b b) (* (* 3 a) c))
0.2b
(* 3 (* c a))

rewrite118.0ms

Algorithm
rewrite-expression-head
Rules
45×add-cbrt-cube add-exp-log
21×prod-exp cbrt-unprod
10×pow1
9×cbrt-undiv div-exp
7×add-sqr-sqrt
6×*-un-lft-identity add-cube-cbrt add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×flip3-- associate-*l* pow-prod-down sqrt-prod flip--
2×sqrt-div associate-*r/ associate-/r/
1×rem-sqrt-square clear-num associate-/r* sub-neg frac-2neg sqrt-pow1 times-frac pow1/2 fma-neg diff-log associate-*r* prod-diff *-commutative div-inv associate-/l*
Counts
4 → 92
Calls
4 calls:
Slowest
47.0ms
(/ (* 3 (* c a)) (* (* 3 a) (- (- b) (sqrt (- (* b b) (* (* 3 a) c))))))
28.0ms
(* 3 (* c a))
25.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
16.0ms
(- (* b b) (* (* 3 a) c))

series478.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
268.0ms
(/ (* 3 (* c a)) (* (* 3 a) (- (- b) (sqrt (- (* b b) (* (* 3 a) c))))))
118.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
59.0ms
(- (* b b) (* (* 3 a) c))
32.0ms
(* 3 (* c a))

simplify12.7s

Counts
53 → 104
Calls
53 calls:
Slowest
3.7s
(/ (* (* (* 3 3) 3) (* (* (* c a) (* c a)) (* c a))) (* (* (* (* 3 a) (* 3 a)) (* 3 a)) (* (* (- (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (- (- b) (sqrt (- (* b b) (* (* 3 a) c))))) (- (- b) (sqrt (- (* b b) (* (* 3 a) c)))))))
575.0ms
(- (+ (log 3) (+ (log c) (log a))) (+ (+ (log 3) (log a)) (log (- (- b) (sqrt (- (* b b) (* (* 3 a) c)))))))
541.0ms
(- (+ (log 3) (log (* c a))) (+ (+ (log 3) (log a)) (log (- (- b) (sqrt (- (* b b) (* (* 3 a) c)))))))
540.0ms
(* (* (* 3 3) 3) (* (* (* c a) (* c a)) (* c a)))
463.0ms
(- (+ (log 3) (+ (log c) (log a))) (+ (log (* 3 a)) (log (- (- b) (sqrt (- (* b b) (* (* 3 a) c)))))))

prune1.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.4b

localize35.0ms

Local error

Found 4 expressions with local error:

24.0b
(sqrt (- (* b b) (* (* 3 a) c)))
1.2b
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
0.4b
(- (* b b) (* (* 3 a) c))
0.2b
(* (* 3 a) c)

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
10×add-sqr-sqrt pow1 fma-def add-log-exp
9×add-cbrt-cube add-exp-log add-cube-cbrt
4×expm1-log1p-u distribute-rgt-neg-in insert-posit16 log1p-expm1-u
3×distribute-lft-neg-in associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
2×sum-log flip3-- sqrt-div flip-- distribute-lft-out
1×neg-sub0 +-commutative rem-sqrt-square neg-mul-1 sub-neg sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log associate-*l* prod-diff neg-log *-commutative associate-+l- flip-+
Counts
4 → 84
Calls
4 calls:
Slowest
27.0ms
(* (* 3 a) c)
14.0ms
(- (* b b) (* (* 3 a) c))
14.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
9.0ms
(sqrt (- (* b b) (* (* 3 a) c)))

series301.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
123.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
88.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
55.0ms
(- (* b b) (* (* 3 a) c))
34.0ms
(* (* 3 a) c)

simplify3.7s

Counts
41 → 96
Calls
41 calls:
Slowest
490.0ms
(* (* (* (* 3 3) 3) (* (* a a) a)) (* (* c c) c))
478.0ms
(* (* (* (* 3 a) (* 3 a)) (* 3 a)) (* (* c c) c))
336.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))
255.0ms
(/ (exp (* b b)) (exp (* (* 3 a) c)))
234.0ms
(- b (* 3/2 (/ (* a c) b)))

prune1.2s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.4b

localize51.0ms

Local error

Found 4 expressions with local error:

24.0b
(sqrt (fma (* a c) -3 (* b b)))
1.2b
(+ (- b) (sqrt (fma (* a c) -3 (* b b))))
0.5b
(fma (* a c) -3 (* b b))
0.1b
(/ (/ (+ (- b) (sqrt (fma (* a c) -3 (* b b)))) 3) a)

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
117×times-frac
116×*-un-lft-identity
65×add-sqr-sqrt
64×add-cube-cbrt
26×distribute-lft-out
19×associate-/l*
16×distribute-rgt-neg-in
10×fma-def
9×add-cbrt-cube add-exp-log
8×add-log-exp
5×pow1 div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×distribute-lft-neg-in cbrt-undiv associate-/r* div-exp sqrt-prod
2×neg-sub0 sum-log div-sub associate-+l-
1×+-commutative rem-sqrt-square clear-num neg-mul-1 frac-2neg sqrt-pow1 flip3-+ pow1/2 neg-log flip-+ fma-udef associate-/l/
Counts
4 → 153
Calls
4 calls:
Slowest
31.0ms
(/ (/ (+ (- b) (sqrt (fma (* a c) -3 (* b b)))) 3) a)
16.0ms
(+ (- b) (sqrt (fma (* a c) -3 (* b b))))
3.0ms
(sqrt (fma (* a c) -3 (* b b)))
0.0ms
(fma (* a c) -3 (* b b))

series487.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
154.0ms
(/ (/ (+ (- b) (sqrt (fma (* a c) -3 (* b b)))) 3) a)
128.0ms
(sqrt (fma (* a c) -3 (* b b)))
121.0ms
(+ (- b) (sqrt (fma (* a c) -3 (* b b))))
85.0ms
(fma (* a c) -3 (* b b))

simplify12.3s

Counts
168 → 165
Calls
168 calls:
Slowest
491.0ms
(/ (/ (* (cbrt (+ (- b) (sqrt (fma (* a c) -3 (* b b))))) (cbrt (+ (- b) (sqrt (fma (* a c) -3 (* b b)))))) (* (cbrt 3) (cbrt 3))) (* (cbrt a) (cbrt a)))
464.0ms
(/ (/ (sqrt (+ (- b) (sqrt (fma (* a c) -3 (* b b))))) (sqrt 3)) (* (cbrt a) (cbrt a)))
226.0ms
(/ (/ (* (cbrt (+ (- b) (sqrt (fma (* a c) -3 (* b b))))) (cbrt (+ (- b) (sqrt (fma (* a c) -3 (* b b)))))) (* (cbrt 3) (cbrt 3))) (sqrt a))
208.0ms
(/ (/ (* (cbrt (+ (- b) (sqrt (fma (* a c) -3 (* b b))))) (cbrt (+ (- b) (sqrt (fma (* a c) -3 (* b b)))))) (* (cbrt 3) (cbrt 3))) 1)
205.0ms
(/ (/ (* (* (+ (- b) (sqrt (fma (* a c) -3 (* b b)))) (+ (- b) (sqrt (fma (* a c) -3 (* b b))))) (+ (- b) (sqrt (fma (* a c) -3 (* b b))))) (* (* 3 3) 3)) (* (* a a) a))

prune2.0s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 5.4b

regimes814.0ms

Accuracy

84.4% (4.6b remaining)

Error of 10.3b against oracle of 5.7b and baseline of 35.5b

bsearch272.0ms

end0.0ms

sample4.2s

Algorithm
intervals
Results
1.1s1084×body2560valid
995.0ms865×body1280valid
828.0ms5877×body80valid
330.0ms2872×body80nan
232.0ms475×body640valid
174.0ms239×body320valid
78.0ms93×body5120valid
23.0ms101×body160valid